Characterization of orthomaps on the Cayley plane

Characterization of orthomaps on the Cayley plane We classify maps which preserve orthogonality on the Cayley projective plane over octonions. In addition, we also classify orthogonality preserving maps on finite dimensional projective spaces over reals, complexes, or quaternions. Unlike similar results which extend Uhlhorns’s theorem we assume neither injectivity/surjectivity nor that orthogonality is preserved in both directions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png aequationes mathematicae Springer Journals

Characterization of orthomaps on the Cayley plane

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Publisher
Springer International Publishing
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Combinatorics
ISSN
0001-9054
eISSN
1420-8903
D.O.I.
10.1007/s00010-017-0532-5
Publisher site
See Article on Publisher Site

Abstract

We classify maps which preserve orthogonality on the Cayley projective plane over octonions. In addition, we also classify orthogonality preserving maps on finite dimensional projective spaces over reals, complexes, or quaternions. Unlike similar results which extend Uhlhorns’s theorem we assume neither injectivity/surjectivity nor that orthogonality is preserved in both directions.

Journal

aequationes mathematicaeSpringer Journals

Published: Jan 20, 2018

References

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